Organisations have shown a significant interest in the adoption of virtualisation technology for improving the efficiency of their Data Centres (DC) from both the resource performance and cost efficiency viewpoints. By improving the efficiency of data centres we can sustainably manage their impact on the environment by controlling their energy consumption. The intentions are clear but how best to approach to Data Centre virtualisation is not. This paper proposes an integrated Enterprise Architecture and Information Infrastructure (EAII) driven approach to guide the Data Centre virtualisation. The EAII approach has been developed based on the review and analysis of well-known The Open Group Architecture Framework (TOGAF) and Information Infrastructure (II) model. The proposed integrated EAII approach seems appropriate to guide and align business strategy and virtualisation implementation for data centres of any size in any industry vertical.